Answering a question of Wilf, we show that, if n is sufficiently large, then one cannot cover an n x p(n) rectangle using each of the p(n) distinct Ferrers shapes of size n exactly once. Moreover, the maximum number of pairwise distinct, non-overlapping Ferrers shapes that can be packed in such a rectangle is only Θ(p(n)/log n).
ASJC Scopus subject areas
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics